Details

analyze779.0ms (8.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample1.8s (19.1%)

Results

1.6s	8256×	body	128	valid
178.0ms	1018×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

740×	`rules-20_binary64`
631×	`fma-neg_binary64`
348×	`rules-15-rev_binary64`
249×	`rules-1_binary64`
232×	`rules-10-rev_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	37	58
2	72	58
3	144	58
4	525	58
5	1935	58
6	4599	58
7	4973	58
8	5023	58

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

20.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))

Status

Error

Program

▶

20.3b

(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

Compiler

Compiled 161 to 99 computations (38.5% saved)

localize73.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	1.5b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series176.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

68.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
54.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
42.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite133.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
175×	`egg-rr`
141×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`

Counts

4 → 175

Calls

4 calls:

129.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
129.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
129.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	68
1	322	68
2	4204	68
3	4996	65
4	4883	65
0	0	0
1	0	0

simplify104.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

483×	`fma-def_binary64`
321×	`fma-neg_binary64`
294×	`rules-20_binary64`
287×	`rules-11_binary64`
272×	`rules-13_binary64`

Counts

271 → 230

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	2275
1	259	2191
2	1093	2165
3	4894	2165
4	5000	2165
5	4990	2165

prune696.0ms (7.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	338	13	351
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	339	13	352

Error

3.9b

Counts

352 → 13

Alt Table

Status	Error	Program
	25.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (exp.f64 (log.f64 (+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (*.f64 4 a) c)))) (neg.f64 b))))))
	34.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a)))))))
	24.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (+.f64 1 (/.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))))))))
	29.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (/.f64 (fma.f64 1/2 (.f64 b b) (neg.f64 (.f64 4 (.f64 c a)))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	24.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) (.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	20.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4) (neg.f64 b))))
▶	19.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	32.0b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (-.f64 (/.f64 (fma.f64 1/2 (.f64 b b) (neg.f64 (.f64 4 (.f64 c a)))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))) b)))
	21.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	25.7b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (*.f64 4 a) c)))))))))
	28.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	23.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (.f64 -1 b))))
	20.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))

Compiler

Compiled 17941 to 10775 computations (39.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series258.0ms (2.7%)

Counts

1 → 20

Calls

1 calls:

258.0ms

(/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

rewrite85.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

279×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
152×	`log1p-expm1-u_binary64`
152×	`expm1-log1p-u_binary64`
147×	`add-cbrt-cube_binary64`

Counts

1 → 34

Calls

1 calls:

84.0ms

(/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	364	26
2	4585	26
3	4908	26
0	0	0
1	0	0

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-neg_binary64`
538×	`rules-15-rev_binary64`
409×	`rules-21_binary64`
319×	`fma-def_binary64`
206×	`rules-13_binary64`

Counts

54 → 55

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	597
1	193	554
2	698	554
3	3626	554
4	5850	554

prune433.0ms (4.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	220	4	224
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	223	14	237

Error

3.6b

Counts

237 → 14

Alt Table

Status	Error	Program
	25.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (exp.f64 (log.f64 (+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (*.f64 4 a) c)))) (neg.f64 b))))))
	34.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a)))))))
	22.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 -1 (/.f64 c b)))
	32.0b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (-.f64 (/.f64 (fma.f64 1/2 (.f64 b b) (neg.f64 (.f64 4 (.f64 c a)))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))) b)))
	30.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (cbrt.f64 (pow.f64 (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) 3)))
	24.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) (.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
▶	20.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4) (neg.f64 b))))
	36.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 2 (fma.f64 b (/.f64 c (neg.f64 (.f64 4 (.f64 a c)))) (/.f64 c (sqrt.f64 (neg.f64 (.f64 4 (.f64 a c))))))))
	29.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (/.f64 (fma.f64 1/2 (.f64 b b) (neg.f64 (.f64 4 (.f64 c a)))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	21.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	25.7b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (*.f64 4 a) c)))))))))
	28.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	20.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	30.7b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (pow.f64 (sqrt.f64 (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))) 2))

Compiler

Compiled 9720 to 5699 computations (41.4% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.5b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	15.8b	(fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b))
	24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	25.0b	(pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4)

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series167.0ms (1.8%)

Counts

2 → 72

Calls

2 calls:

111.0ms	(fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b))
56.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4)

rewrite75.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

966×	`prod-diff_binary64`
133×	`add-sqr-sqrt_binary64`
131×	`log1p-expm1-u_binary64`
131×	`expm1-log1p-u_binary64`
126×	`add-cbrt-cube_binary64`

Counts

2 → 61

Calls

2 calls:

73.0ms	(fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b))
73.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	53
1	316	36
2	3835	36
3	5547	36
0	0	0
1	0	0

simplify100.0ms (1%)

Algorithm

1×	egg-herbie

Rules

371×	`fma-neg_binary64`
300×	`fma-def_binary64`
247×	`rules-4_binary64`
231×	`rules-20_binary64`
219×	`rules-13_binary64`

Counts

133 → 170

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	303	3926
1	982	3889
2	4596	3889
3	5051	3889

prune1.1s (11.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	368	2	370
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	369	15	384

Error

2.6b

Counts

384 → 15

Alt Table

Status	Error	Program
	25.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (exp.f64 (log.f64 (+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (*.f64 4 a) c)))) (neg.f64 b))))))
	34.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a)))))))
	22.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 -1 (/.f64 c b)))
	32.0b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (-.f64 (/.f64 (fma.f64 1/2 (.f64 b b) (neg.f64 (.f64 4 (.f64 c a)))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))) b)))
	30.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (cbrt.f64 (pow.f64 (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) 3)))
	40.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (-.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2) b)))
	24.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) (.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
✓	20.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4) (neg.f64 b))))
	36.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 2 (fma.f64 b (/.f64 c (neg.f64 (.f64 4 (.f64 a c)))) (/.f64 c (sqrt.f64 (neg.f64 (.f64 4 (.f64 a c))))))))
	38.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (-.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2) b)))
	29.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (/.f64 (fma.f64 1/2 (.f64 b b) (neg.f64 (.f64 4 (.f64 c a)))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	21.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	28.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
▶	20.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	30.7b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (pow.f64 (sqrt.f64 (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))) 2))

Compiler

Compiled 25281 to 15769 computations (37.6% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	12.8b	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4) 2))
	24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
	25.0b	(pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4)

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series87.0ms (0.9%)

Counts

1 → 20

Calls

1 calls:

87.0ms

(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 1/4) 2))

rewrite74.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

266×	`expm1-udef_binary64`
266×	`log1p-udef_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`
149×	`add-sqr-sqrt_binary64`

Counts

1 → 36

Calls

1 calls:

73.0ms

(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 1/4) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	369	20
2	4307	20
3	4907	20
0	0	0
1	0	0

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-neg_binary64`
426×	`fma-def_binary64`
421×	`rules-21_binary64`
289×	`rules-4_binary64`
242×	`rules-13_binary64`

Counts

56 → 58

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	608
1	190	576
2	748	554
3	3874	554
4	5001	554

prune852.0ms (8.9%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	245	15	260

Error

0.7b

Counts

260 → 15

Alt Table

Status	Error	Program
	25.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (exp.f64 (log.f64 (+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (*.f64 4 a) c)))) (neg.f64 b))))))
	34.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a)))))))
	22.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 -1 (/.f64 c b)))
	32.0b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (-.f64 (/.f64 (fma.f64 1/2 (.f64 b b) (neg.f64 (.f64 4 (.f64 c a)))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))) b)))
	30.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (cbrt.f64 (pow.f64 (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) 3)))
	40.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (-.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2) b)))
	30.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 a 4)) (log.f64 (/.f64 -1 c))))) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	30.7b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (pow.f64 (sqrt.f64 (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))) 2))
	24.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) (.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
✓	20.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4) (neg.f64 b))))
	36.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 2 (fma.f64 b (/.f64 c (neg.f64 (.f64 4 (.f64 a c)))) (/.f64 c (sqrt.f64 (neg.f64 (.f64 4 (.f64 a c))))))))
	38.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (-.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2) b)))
	29.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (/.f64 (fma.f64 1/2 (.f64 b b) (neg.f64 (.f64 4 (.f64 c a)))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	28.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
✓	20.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))

Compiler

Compiled 14054 to 8838 computations (37.1% saved)

regimes1.7s (18.1%)

Accuracy

Total 7.1b remaining (91.1%)

Threshold costs 0b (0%)

Counts

143 → 5

Compiler

Compiled 23370 to 16002 computations (31.5% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 41 to 26 computations (36.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	487
1	58	487

end566.0ms (5.9%)

Compiler: Compiled 1292 to 822 computations (36.4% saved)

Details

analyze779.0ms (8.2%)

sample1.8s (19.1%)

simplify67.0ms (0.7%)

prune4.0ms (0%)

localize73.0ms (0.8%)

series176.0ms (1.8%)

rewrite133.0ms (1.4%)

simplify104.0ms (1.1%)

prune696.0ms (7.3%)

localize21.0ms (0.2%)

series258.0ms (2.7%)

rewrite85.0ms (0.9%)

simplify52.0ms (0.5%)

prune433.0ms (4.5%)

localize27.0ms (0.3%)

series167.0ms (1.8%)

rewrite75.0ms (0.8%)

simplify100.0ms (1%)

prune1.1s (11.3%)

localize25.0ms (0.3%)

series87.0ms (0.9%)

rewrite74.0ms (0.8%)

simplify48.0ms (0.5%)

prune852.0ms (8.9%)

regimes1.7s (18.1%)

bsearch10.0ms (0.1%)

simplify5.0ms (0.1%)

end566.0ms (5.9%)

Profiling